algebra.dual_quaternion ⟷ Mathlib.Algebra.DualQuaternion

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,8 +3,8 @@ Copyright (c) 2023 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.Algebra.DualNumber
-import Mathbin.Algebra.Quaternion
+import Algebra.DualNumber
+import Algebra.Quaternion
 
 #align_import algebra.dual_quaternion from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,15 +2,12 @@
 Copyright (c) 2023 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module algebra.dual_quaternion
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.DualNumber
 import Mathbin.Algebra.Quaternion
 
+#align_import algebra.dual_quaternion from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
 /-!
 # Dual quaternions
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -35,6 +35,7 @@ variable {R : Type _} [CommRing R]
 
 namespace Quaternion
 
+#print Quaternion.dualNumberEquiv /-
 /-- The dual quaternions can be equivalently represented as a quaternion with dual coefficients,
 or as a dual number with quaternion coefficients.
 
@@ -60,106 +61,139 @@ def dualNumberEquiv : Quaternion (DualNumber R) ≃ₐ[R] DualNumber (Quaternion
     rfl
   commutes' r := rfl
 #align quaternion.dual_number_equiv Quaternion.dualNumberEquiv
+-/
 
 /-! Lemmas characterizing `quaternion.dual_number_equiv`. -/
 
 
+#print Quaternion.re_fst_dualNumberEquiv /-
 -- `simps` can't work on `dual_number` because it's not a structure
 @[simp]
 theorem re_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).fst.re = q.re.fst :=
   rfl
 #align quaternion.re_fst_dual_number_equiv Quaternion.re_fst_dualNumberEquiv
+-/
 
+#print Quaternion.imI_fst_dualNumberEquiv /-
 @[simp]
 theorem imI_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).fst.imI = q.imI.fst :=
   rfl
 #align quaternion.im_i_fst_dual_number_equiv Quaternion.imI_fst_dualNumberEquiv
+-/
 
+#print Quaternion.imJ_fst_dualNumberEquiv /-
 @[simp]
 theorem imJ_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).fst.imJ = q.imJ.fst :=
   rfl
 #align quaternion.im_j_fst_dual_number_equiv Quaternion.imJ_fst_dualNumberEquiv
+-/
 
+#print Quaternion.imK_fst_dualNumberEquiv /-
 @[simp]
 theorem imK_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).fst.imK = q.imK.fst :=
   rfl
 #align quaternion.im_k_fst_dual_number_equiv Quaternion.imK_fst_dualNumberEquiv
+-/
 
+#print Quaternion.re_snd_dualNumberEquiv /-
 @[simp]
 theorem re_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).snd.re = q.re.snd :=
   rfl
 #align quaternion.re_snd_dual_number_equiv Quaternion.re_snd_dualNumberEquiv
+-/
 
+#print Quaternion.imI_snd_dualNumberEquiv /-
 @[simp]
 theorem imI_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).snd.imI = q.imI.snd :=
   rfl
 #align quaternion.im_i_snd_dual_number_equiv Quaternion.imI_snd_dualNumberEquiv
+-/
 
+#print Quaternion.imJ_snd_dualNumberEquiv /-
 @[simp]
 theorem imJ_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).snd.imJ = q.imJ.snd :=
   rfl
 #align quaternion.im_j_snd_dual_number_equiv Quaternion.imJ_snd_dualNumberEquiv
+-/
 
+#print Quaternion.imK_snd_dualNumberEquiv /-
 @[simp]
 theorem imK_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).snd.imK = q.imK.snd :=
   rfl
 #align quaternion.im_k_snd_dual_number_equiv Quaternion.imK_snd_dualNumberEquiv
+-/
 
+#print Quaternion.fst_re_dualNumberEquiv_symm /-
 @[simp]
 theorem fst_re_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).re.fst = d.fst.re :=
   rfl
 #align quaternion.fst_re_dual_number_equiv_symm Quaternion.fst_re_dualNumberEquiv_symm
+-/
 
+#print Quaternion.fst_imI_dualNumberEquiv_symm /-
 @[simp]
 theorem fst_imI_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imI.fst = d.fst.imI :=
   rfl
 #align quaternion.fst_im_i_dual_number_equiv_symm Quaternion.fst_imI_dualNumberEquiv_symm
+-/
 
+#print Quaternion.fst_imJ_dualNumberEquiv_symm /-
 @[simp]
 theorem fst_imJ_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imJ.fst = d.fst.imJ :=
   rfl
 #align quaternion.fst_im_j_dual_number_equiv_symm Quaternion.fst_imJ_dualNumberEquiv_symm
+-/
 
+#print Quaternion.fst_imK_dualNumberEquiv_symm /-
 @[simp]
 theorem fst_imK_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imK.fst = d.fst.imK :=
   rfl
 #align quaternion.fst_im_k_dual_number_equiv_symm Quaternion.fst_imK_dualNumberEquiv_symm
+-/
 
+#print Quaternion.snd_re_dualNumberEquiv_symm /-
 @[simp]
 theorem snd_re_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).re.snd = d.snd.re :=
   rfl
 #align quaternion.snd_re_dual_number_equiv_symm Quaternion.snd_re_dualNumberEquiv_symm
+-/
 
+#print Quaternion.snd_imI_dualNumberEquiv_symm /-
 @[simp]
 theorem snd_imI_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imI.snd = d.snd.imI :=
   rfl
 #align quaternion.snd_im_i_dual_number_equiv_symm Quaternion.snd_imI_dualNumberEquiv_symm
+-/
 
+#print Quaternion.snd_imJ_dualNumberEquiv_symm /-
 @[simp]
 theorem snd_imJ_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imJ.snd = d.snd.imJ :=
   rfl
 #align quaternion.snd_im_j_dual_number_equiv_symm Quaternion.snd_imJ_dualNumberEquiv_symm
+-/
 
+#print Quaternion.snd_imK_dualNumberEquiv_symm /-
 @[simp]
 theorem snd_imK_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imK.snd = d.snd.imK :=
   rfl
 #align quaternion.snd_im_k_dual_number_equiv_symm Quaternion.snd_imK_dualNumberEquiv_symm
+-/
 
 end Quaternion
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -35,9 +35,6 @@ variable {R : Type _} [CommRing R]
 
 namespace Quaternion
 
-/- warning: quaternion.dual_number_equiv -> Quaternion.dualNumberEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.dual_number_equiv Quaternion.dualNumberEquivₓ'. -/
 /-- The dual quaternions can be equivalently represented as a quaternion with dual coefficients,
 or as a dual number with quaternion coefficients.
 
@@ -67,9 +64,6 @@ def dualNumberEquiv : Quaternion (DualNumber R) ≃ₐ[R] DualNumber (Quaternion
 /-! Lemmas characterizing `quaternion.dual_number_equiv`. -/
 
 
-/- warning: quaternion.re_fst_dual_number_equiv -> Quaternion.re_fst_dualNumberEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.re_fst_dual_number_equiv Quaternion.re_fst_dualNumberEquivₓ'. -/
 -- `simps` can't work on `dual_number` because it's not a structure
 @[simp]
 theorem re_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -77,135 +71,90 @@ theorem re_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
   rfl
 #align quaternion.re_fst_dual_number_equiv Quaternion.re_fst_dualNumberEquiv
 
-/- warning: quaternion.im_i_fst_dual_number_equiv -> Quaternion.imI_fst_dualNumberEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.im_i_fst_dual_number_equiv Quaternion.imI_fst_dualNumberEquivₓ'. -/
 @[simp]
 theorem imI_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).fst.imI = q.imI.fst :=
   rfl
 #align quaternion.im_i_fst_dual_number_equiv Quaternion.imI_fst_dualNumberEquiv
 
-/- warning: quaternion.im_j_fst_dual_number_equiv -> Quaternion.imJ_fst_dualNumberEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.im_j_fst_dual_number_equiv Quaternion.imJ_fst_dualNumberEquivₓ'. -/
 @[simp]
 theorem imJ_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).fst.imJ = q.imJ.fst :=
   rfl
 #align quaternion.im_j_fst_dual_number_equiv Quaternion.imJ_fst_dualNumberEquiv
 
-/- warning: quaternion.im_k_fst_dual_number_equiv -> Quaternion.imK_fst_dualNumberEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.im_k_fst_dual_number_equiv Quaternion.imK_fst_dualNumberEquivₓ'. -/
 @[simp]
 theorem imK_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).fst.imK = q.imK.fst :=
   rfl
 #align quaternion.im_k_fst_dual_number_equiv Quaternion.imK_fst_dualNumberEquiv
 
-/- warning: quaternion.re_snd_dual_number_equiv -> Quaternion.re_snd_dualNumberEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.re_snd_dual_number_equiv Quaternion.re_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem re_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).snd.re = q.re.snd :=
   rfl
 #align quaternion.re_snd_dual_number_equiv Quaternion.re_snd_dualNumberEquiv
 
-/- warning: quaternion.im_i_snd_dual_number_equiv -> Quaternion.imI_snd_dualNumberEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.im_i_snd_dual_number_equiv Quaternion.imI_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem imI_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).snd.imI = q.imI.snd :=
   rfl
 #align quaternion.im_i_snd_dual_number_equiv Quaternion.imI_snd_dualNumberEquiv
 
-/- warning: quaternion.im_j_snd_dual_number_equiv -> Quaternion.imJ_snd_dualNumberEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.im_j_snd_dual_number_equiv Quaternion.imJ_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem imJ_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).snd.imJ = q.imJ.snd :=
   rfl
 #align quaternion.im_j_snd_dual_number_equiv Quaternion.imJ_snd_dualNumberEquiv
 
-/- warning: quaternion.im_k_snd_dual_number_equiv -> Quaternion.imK_snd_dualNumberEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.im_k_snd_dual_number_equiv Quaternion.imK_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem imK_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).snd.imK = q.imK.snd :=
   rfl
 #align quaternion.im_k_snd_dual_number_equiv Quaternion.imK_snd_dualNumberEquiv
 
-/- warning: quaternion.fst_re_dual_number_equiv_symm -> Quaternion.fst_re_dualNumberEquiv_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.fst_re_dual_number_equiv_symm Quaternion.fst_re_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_re_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).re.fst = d.fst.re :=
   rfl
 #align quaternion.fst_re_dual_number_equiv_symm Quaternion.fst_re_dualNumberEquiv_symm
 
-/- warning: quaternion.fst_im_i_dual_number_equiv_symm -> Quaternion.fst_imI_dualNumberEquiv_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.fst_im_i_dual_number_equiv_symm Quaternion.fst_imI_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_imI_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imI.fst = d.fst.imI :=
   rfl
 #align quaternion.fst_im_i_dual_number_equiv_symm Quaternion.fst_imI_dualNumberEquiv_symm
 
-/- warning: quaternion.fst_im_j_dual_number_equiv_symm -> Quaternion.fst_imJ_dualNumberEquiv_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.fst_im_j_dual_number_equiv_symm Quaternion.fst_imJ_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_imJ_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imJ.fst = d.fst.imJ :=
   rfl
 #align quaternion.fst_im_j_dual_number_equiv_symm Quaternion.fst_imJ_dualNumberEquiv_symm
 
-/- warning: quaternion.fst_im_k_dual_number_equiv_symm -> Quaternion.fst_imK_dualNumberEquiv_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.fst_im_k_dual_number_equiv_symm Quaternion.fst_imK_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_imK_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imK.fst = d.fst.imK :=
   rfl
 #align quaternion.fst_im_k_dual_number_equiv_symm Quaternion.fst_imK_dualNumberEquiv_symm
 
-/- warning: quaternion.snd_re_dual_number_equiv_symm -> Quaternion.snd_re_dualNumberEquiv_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.snd_re_dual_number_equiv_symm Quaternion.snd_re_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_re_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).re.snd = d.snd.re :=
   rfl
 #align quaternion.snd_re_dual_number_equiv_symm Quaternion.snd_re_dualNumberEquiv_symm
 
-/- warning: quaternion.snd_im_i_dual_number_equiv_symm -> Quaternion.snd_imI_dualNumberEquiv_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.snd_im_i_dual_number_equiv_symm Quaternion.snd_imI_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_imI_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imI.snd = d.snd.imI :=
   rfl
 #align quaternion.snd_im_i_dual_number_equiv_symm Quaternion.snd_imI_dualNumberEquiv_symm
 
-/- warning: quaternion.snd_im_j_dual_number_equiv_symm -> Quaternion.snd_imJ_dualNumberEquiv_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.snd_im_j_dual_number_equiv_symm Quaternion.snd_imJ_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_imJ_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imJ.snd = d.snd.imJ :=
   rfl
 #align quaternion.snd_im_j_dual_number_equiv_symm Quaternion.snd_imJ_dualNumberEquiv_symm
 
-/- warning: quaternion.snd_im_k_dual_number_equiv_symm -> Quaternion.snd_imK_dualNumberEquiv_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quaternion.snd_im_k_dual_number_equiv_symm Quaternion.snd_imK_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_imK_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imK.snd = d.snd.imK :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -36,10 +36,7 @@ variable {R : Type _} [CommRing R]
 namespace Quaternion
 
 /- warning: quaternion.dual_number_equiv -> Quaternion.dualNumberEquiv is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R 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(Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))
-but is expected to have type
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(CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R 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(IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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_inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.dual_number_equiv Quaternion.dualNumberEquivₓ'. -/
 /-- The dual quaternions can be equivalently represented as a quaternion with dual coefficients,
 or as a dual number with quaternion coefficients.
@@ -71,10 +68,7 @@ def dualNumberEquiv : Quaternion (DualNumber R) ≃ₐ[R] DualNumber (Quaternion
 
 
 /- warning: quaternion.re_fst_dual_number_equiv -> Quaternion.re_fst_dualNumberEquiv is a dubious translation:
-lean 3 declaration is
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(AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} 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(Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) 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_inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.re_fst_dual_number_equiv Quaternion.re_fst_dualNumberEquivₓ'. -/
 -- `simps` can't work on `dual_number` because it's not a structure
 @[simp]
@@ -84,10 +78,7 @@ theorem re_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 #align quaternion.re_fst_dual_number_equiv Quaternion.re_fst_dualNumberEquiv
 
 /- warning: quaternion.im_i_fst_dual_number_equiv -> Quaternion.imI_fst_dualNumberEquiv is a dubious translation:
-lean 3 declaration is
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R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.im_i_fst_dual_number_equiv Quaternion.imI_fst_dualNumberEquivₓ'. -/
 @[simp]
 theorem imI_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -96,10 +87,7 @@ theorem imI_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 #align quaternion.im_i_fst_dual_number_equiv Quaternion.imI_fst_dualNumberEquiv
 
 /- warning: quaternion.im_j_fst_dual_number_equiv -> Quaternion.imJ_fst_dualNumberEquiv is a dubious translation:
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(TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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_inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.im_j_fst_dual_number_equiv Quaternion.imJ_fst_dualNumberEquivₓ'. -/
 @[simp]
 theorem imJ_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -108,10 +96,7 @@ theorem imJ_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 #align quaternion.im_j_fst_dual_number_equiv Quaternion.imJ_fst_dualNumberEquiv
 
 /- warning: quaternion.im_k_fst_dual_number_equiv -> Quaternion.imK_fst_dualNumberEquiv is a dubious translation:
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(AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} 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-but is expected to have type
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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.im_k_fst_dual_number_equiv Quaternion.imK_fst_dualNumberEquivₓ'. -/
 @[simp]
 theorem imK_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -120,10 +105,7 @@ theorem imK_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 #align quaternion.im_k_fst_dual_number_equiv Quaternion.imK_fst_dualNumberEquiv
 
 /- warning: quaternion.re_snd_dual_number_equiv -> Quaternion.re_snd_dualNumberEquiv is a dubious translation:
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(Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) 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(AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R 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R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} 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(AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} 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u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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_inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.re_snd_dual_number_equiv Quaternion.re_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem re_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -132,10 +114,7 @@ theorem re_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 #align quaternion.re_snd_dual_number_equiv Quaternion.re_snd_dualNumberEquiv
 
 /- warning: quaternion.im_i_snd_dual_number_equiv -> Quaternion.imI_snd_dualNumberEquiv is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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_inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.im_i_snd_dual_number_equiv Quaternion.imI_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem imI_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -144,10 +123,7 @@ theorem imI_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 #align quaternion.im_i_snd_dual_number_equiv Quaternion.imI_snd_dualNumberEquiv
 
 /- warning: quaternion.im_j_snd_dual_number_equiv -> Quaternion.imJ_snd_dualNumberEquiv is a dubious translation:
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(TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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_inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.im_j_snd_dual_number_equiv Quaternion.imJ_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem imJ_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -156,10 +132,7 @@ theorem imJ_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 #align quaternion.im_j_snd_dual_number_equiv Quaternion.imJ_snd_dualNumberEquiv
 
 /- warning: quaternion.im_k_snd_dual_number_equiv -> Quaternion.imK_snd_dualNumberEquiv is a dubious translation:
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(AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} 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-but is expected to have type
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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.im_k_snd_dual_number_equiv Quaternion.imK_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem imK_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -168,10 +141,7 @@ theorem imK_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 #align quaternion.im_k_snd_dual_number_equiv Quaternion.imK_snd_dualNumberEquiv
 
 /- warning: quaternion.fst_re_dual_number_equiv_symm -> Quaternion.fst_re_dualNumberEquiv_symm is a dubious translation:
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(SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1)))) => (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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(SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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-but is expected to have type
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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.fst_re_dual_number_equiv_symm Quaternion.fst_re_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_re_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
@@ -180,10 +150,7 @@ theorem fst_re_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
 #align quaternion.fst_re_dual_number_equiv_symm Quaternion.fst_re_dualNumberEquiv_symm
 
 /- warning: quaternion.fst_im_i_dual_number_equiv_symm -> Quaternion.fst_imI_dualNumberEquiv_symm is a dubious translation:
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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1)))) => (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R 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(NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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(AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.fst_im_i_dual_number_equiv_symm Quaternion.fst_imI_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_imI_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
@@ -192,10 +159,7 @@ theorem fst_imI_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
 #align quaternion.fst_im_i_dual_number_equiv_symm Quaternion.fst_imI_dualNumberEquiv_symm
 
 /- warning: quaternion.fst_im_j_dual_number_equiv_symm -> Quaternion.fst_imJ_dualNumberEquiv_symm is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.fst_im_j_dual_number_equiv_symm Quaternion.fst_imJ_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_imJ_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
@@ -204,10 +168,7 @@ theorem fst_imJ_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
 #align quaternion.fst_im_j_dual_number_equiv_symm Quaternion.fst_imJ_dualNumberEquiv_symm
 
 /- warning: quaternion.fst_im_k_dual_number_equiv_symm -> Quaternion.fst_imK_dualNumberEquiv_symm is a dubious translation:
-lean 3 declaration is
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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.fst_im_k_dual_number_equiv_symm Quaternion.fst_imK_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_imK_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
@@ -216,10 +177,7 @@ theorem fst_imK_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
 #align quaternion.fst_im_k_dual_number_equiv_symm Quaternion.fst_imK_dualNumberEquiv_symm
 
 /- warning: quaternion.snd_re_dual_number_equiv_symm -> Quaternion.snd_re_dualNumberEquiv_symm is a dubious translation:
-lean 3 declaration is
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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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-but is expected to have type
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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.snd_re_dual_number_equiv_symm Quaternion.snd_re_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_re_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
@@ -228,10 +186,7 @@ theorem snd_re_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
 #align quaternion.snd_re_dual_number_equiv_symm Quaternion.snd_re_dualNumberEquiv_symm
 
 /- warning: quaternion.snd_im_i_dual_number_equiv_symm -> Quaternion.snd_imI_dualNumberEquiv_symm is a dubious translation:
-lean 3 declaration is
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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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-but is expected to have type
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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.snd_im_i_dual_number_equiv_symm Quaternion.snd_imI_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_imI_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
@@ -240,10 +195,7 @@ theorem snd_imI_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
 #align quaternion.snd_im_i_dual_number_equiv_symm Quaternion.snd_imI_dualNumberEquiv_symm
 
 /- warning: quaternion.snd_im_j_dual_number_equiv_symm -> Quaternion.snd_imJ_dualNumberEquiv_symm is a dubious translation:
-lean 3 declaration is
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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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-but is expected to have type
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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.snd_im_j_dual_number_equiv_symm Quaternion.snd_imJ_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_imJ_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
@@ -252,10 +204,7 @@ theorem snd_imJ_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
 #align quaternion.snd_im_j_dual_number_equiv_symm Quaternion.snd_imJ_dualNumberEquiv_symm
 
 /- warning: quaternion.snd_im_k_dual_number_equiv_symm -> Quaternion.snd_imK_dualNumberEquiv_symm is a dubious translation:
-lean 3 declaration is
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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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-but is expected to have type
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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quaternion.snd_im_k_dual_number_equiv_symm Quaternion.snd_imK_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_imK_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -74,7 +74,7 @@ def dualNumberEquiv : Quaternion (DualNumber R) ≃ₐ[R] DualNumber (Quaternion
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} 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(Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) 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R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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_inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
 Case conversion may be inaccurate. Consider using '#align quaternion.re_fst_dual_number_equiv Quaternion.re_fst_dualNumberEquivₓ'. -/
 -- `simps` can't work on `dual_number` because it's not a structure
 @[simp]
@@ -87,7 +87,7 @@ theorem re_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) 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R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) 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R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
 Case conversion may be inaccurate. Consider using '#align quaternion.im_i_fst_dual_number_equiv Quaternion.imI_fst_dualNumberEquivₓ'. -/
 @[simp]
 theorem imI_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -99,7 +99,7 @@ theorem imI_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) 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R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) 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R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
 Case conversion may be inaccurate. Consider using '#align quaternion.im_j_fst_dual_number_equiv Quaternion.imJ_fst_dualNumberEquivₓ'. -/
 @[simp]
 theorem imJ_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -111,7 +111,7 @@ theorem imJ_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) 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R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) 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R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
 Case conversion may be inaccurate. Consider using '#align quaternion.im_k_fst_dual_number_equiv Quaternion.imK_fst_dualNumberEquivₓ'. -/
 @[simp]
 theorem imK_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -123,7 +123,7 @@ theorem imK_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) 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R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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_inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
 Case conversion may be inaccurate. Consider using '#align quaternion.re_snd_dual_number_equiv Quaternion.re_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem re_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -135,7 +135,7 @@ theorem re_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) 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R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) 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R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
 Case conversion may be inaccurate. Consider using '#align quaternion.im_i_snd_dual_number_equiv Quaternion.imI_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem imI_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -147,7 +147,7 @@ theorem imI_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) 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R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) 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R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
 Case conversion may be inaccurate. Consider using '#align quaternion.im_j_snd_dual_number_equiv Quaternion.imJ_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem imJ_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -159,7 +159,7 @@ theorem imJ_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) 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R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) 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R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
 Case conversion may be inaccurate. Consider using '#align quaternion.im_k_snd_dual_number_equiv Quaternion.imK_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem imK_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -171,7 +171,7 @@ theorem imK_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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_inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
 Case conversion may be inaccurate. Consider using '#align quaternion.fst_re_dual_number_equiv_symm Quaternion.fst_re_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_re_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
@@ -183,7 +183,7 @@ theorem fst_re_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1)))) => (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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(SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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(IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
 Case conversion may be inaccurate. Consider using '#align quaternion.fst_im_i_dual_number_equiv_symm Quaternion.fst_imI_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_imI_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
@@ -195,7 +195,7 @@ theorem fst_imI_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R 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(SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1)))) => (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
 Case conversion may be inaccurate. Consider using '#align quaternion.fst_im_j_dual_number_equiv_symm Quaternion.fst_imJ_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_imJ_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
@@ -207,7 +207,7 @@ theorem fst_imJ_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1)))) => (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R 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(NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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_inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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_inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
 Case conversion may be inaccurate. Consider using '#align quaternion.fst_im_k_dual_number_equiv_symm Quaternion.fst_imK_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_imK_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
@@ -219,7 +219,7 @@ theorem fst_imK_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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_inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
 Case conversion may be inaccurate. Consider using '#align quaternion.snd_re_dual_number_equiv_symm Quaternion.snd_re_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_re_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
@@ -231,7 +231,7 @@ theorem snd_re_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1)))) => (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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(SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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(IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
 Case conversion may be inaccurate. Consider using '#align quaternion.snd_im_i_dual_number_equiv_symm Quaternion.snd_imI_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_imI_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
@@ -243,7 +243,7 @@ theorem snd_imI_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1)))) (fun (_x : AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R 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(SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1)))) => (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
 Case conversion may be inaccurate. Consider using '#align quaternion.snd_im_j_dual_number_equiv_symm Quaternion.snd_imJ_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_imJ_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
@@ -255,7 +255,7 @@ theorem snd_imJ_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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(AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1)))) => (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R 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(NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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_inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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_inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
 Case conversion may be inaccurate. Consider using '#align quaternion.snd_im_k_dual_number_equiv_symm Quaternion.snd_imK_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_imK_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module algebra.dual_quaternion
-! leanprover-community/mathlib commit 536c256e5de12c1dc0352b6b60b44f3c6c5ef340
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Algebra.Quaternion
 /-!
 # Dual quaternions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Similar to the way that rotations in 3D space can be represented by quaternions of unit length,
 rigid motions in 3D space can be represented by dual quaternions of unit length.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -32,6 +32,12 @@ variable {R : Type _} [CommRing R]
 
 namespace Quaternion
 
+/- warning: quaternion.dual_number_equiv -> Quaternion.dualNumberEquiv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R], AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R 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(IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align quaternion.dual_number_equiv Quaternion.dualNumberEquivₓ'. -/
 /-- The dual quaternions can be equivalently represented as a quaternion with dual coefficients,
 or as a dual number with quaternion coefficients.
 
@@ -61,6 +67,12 @@ def dualNumberEquiv : Quaternion (DualNumber R) ≃ₐ[R] DualNumber (Quaternion
 /-! Lemmas characterizing `quaternion.dual_number_equiv`. -/
 
 
+/- warning: quaternion.re_fst_dual_number_equiv -> Quaternion.re_fst_dualNumberEquiv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R 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(Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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_inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+Case conversion may be inaccurate. Consider using '#align quaternion.re_fst_dual_number_equiv Quaternion.re_fst_dualNumberEquivₓ'. -/
 -- `simps` can't work on `dual_number` because it's not a structure
 @[simp]
 theorem re_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
@@ -68,90 +80,180 @@ theorem re_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
   rfl
 #align quaternion.re_fst_dual_number_equiv Quaternion.re_fst_dualNumberEquiv
 
+/- warning: quaternion.im_i_fst_dual_number_equiv -> Quaternion.imI_fst_dualNumberEquiv is a dubious translation:
+lean 3 declaration is
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(Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} 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(AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+Case conversion may be inaccurate. Consider using '#align quaternion.im_i_fst_dual_number_equiv Quaternion.imI_fst_dualNumberEquivₓ'. -/
 @[simp]
 theorem imI_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).fst.imI = q.imI.fst :=
   rfl
 #align quaternion.im_i_fst_dual_number_equiv Quaternion.imI_fst_dualNumberEquiv
 
+/- warning: quaternion.im_j_fst_dual_number_equiv -> Quaternion.imJ_fst_dualNumberEquiv is a dubious translation:
+lean 3 declaration is
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(AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R 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(CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+Case conversion may be inaccurate. Consider using '#align quaternion.im_j_fst_dual_number_equiv Quaternion.imJ_fst_dualNumberEquivₓ'. -/
 @[simp]
 theorem imJ_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).fst.imJ = q.imJ.fst :=
   rfl
 #align quaternion.im_j_fst_dual_number_equiv Quaternion.imJ_fst_dualNumberEquiv
 
+/- warning: quaternion.im_k_fst_dual_number_equiv -> Quaternion.imK_fst_dualNumberEquiv is a dubious translation:
+lean 3 declaration is
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(Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) 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(AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R 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R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} 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(AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) 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R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+Case conversion may be inaccurate. Consider using '#align quaternion.im_k_fst_dual_number_equiv Quaternion.imK_fst_dualNumberEquivₓ'. -/
 @[simp]
 theorem imK_fst_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).fst.imK = q.imK.fst :=
   rfl
 #align quaternion.im_k_fst_dual_number_equiv Quaternion.imK_fst_dualNumberEquiv
 
+/- warning: quaternion.re_snd_dual_number_equiv -> Quaternion.re_snd_dualNumberEquiv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) 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R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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_inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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_inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R 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+Case conversion may be inaccurate. Consider using '#align quaternion.re_snd_dual_number_equiv Quaternion.re_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem re_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).snd.re = q.re.snd :=
   rfl
 #align quaternion.re_snd_dual_number_equiv Quaternion.re_snd_dualNumberEquiv
 
+/- warning: quaternion.im_i_snd_dual_number_equiv -> Quaternion.imI_snd_dualNumberEquiv is a dubious translation:
+lean 3 declaration is
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(TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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_inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R 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(Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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_inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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+Case conversion may be inaccurate. Consider using '#align quaternion.im_i_snd_dual_number_equiv Quaternion.imI_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem imI_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).snd.imI = q.imI.snd :=
   rfl
 #align quaternion.im_i_snd_dual_number_equiv Quaternion.imI_snd_dualNumberEquiv
 
+/- warning: quaternion.im_j_snd_dual_number_equiv -> Quaternion.imJ_snd_dualNumberEquiv is a dubious translation:
+lean 3 declaration is
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(AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R 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R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+Case conversion may be inaccurate. Consider using '#align quaternion.im_j_snd_dual_number_equiv Quaternion.imJ_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem imJ_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).snd.imJ = q.imJ.snd :=
   rfl
 #align quaternion.im_j_snd_dual_number_equiv Quaternion.imJ_snd_dualNumberEquiv
 
+/- warning: quaternion.im_k_snd_dual_number_equiv -> Quaternion.imK_snd_dualNumberEquiv is a dubious translation:
+lean 3 declaration is
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(Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) 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(AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R 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R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} 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(AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) => (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) -> (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (AlgEquiv.hasCoeToFun.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.algebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_3.{u1} R _inst_1))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (q : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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_inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) 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R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) 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_inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1) q))) (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) q))
+Case conversion may be inaccurate. Consider using '#align quaternion.im_k_snd_dual_number_equiv Quaternion.imK_snd_dualNumberEquivₓ'. -/
 @[simp]
 theorem imK_snd_dualNumberEquiv (q : Quaternion (DualNumber R)) :
     (dualNumberEquiv q).snd.imK = q.imK.snd :=
   rfl
 #align quaternion.im_k_snd_dual_number_equiv Quaternion.imK_snd_dualNumberEquiv
 
+/- warning: quaternion.fst_re_dual_number_equiv_symm -> Quaternion.fst_re_dualNumberEquiv_symm is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_2.{u1} R _inst_1)) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Quaternion.ring.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_1.{u1} R _inst_1)))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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_inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+Case conversion may be inaccurate. Consider using '#align quaternion.fst_re_dual_number_equiv_symm Quaternion.fst_re_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_re_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).re.fst = d.fst.re :=
   rfl
 #align quaternion.fst_re_dual_number_equiv_symm Quaternion.fst_re_dualNumberEquiv_symm
 
+/- warning: quaternion.fst_im_i_dual_number_equiv_symm -> Quaternion.fst_imI_dualNumberEquiv_symm is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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_inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+Case conversion may be inaccurate. Consider using '#align quaternion.fst_im_i_dual_number_equiv_symm Quaternion.fst_imI_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_imI_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imI.fst = d.fst.imI :=
   rfl
 #align quaternion.fst_im_i_dual_number_equiv_symm Quaternion.fst_imI_dualNumberEquiv_symm
 
+/- warning: quaternion.fst_im_j_dual_number_equiv_symm -> Quaternion.fst_imJ_dualNumberEquiv_symm is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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_inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+Case conversion may be inaccurate. Consider using '#align quaternion.fst_im_j_dual_number_equiv_symm Quaternion.fst_imJ_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_imJ_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imJ.fst = d.fst.imJ :=
   rfl
 #align quaternion.fst_im_j_dual_number_equiv_symm Quaternion.fst_imJ_dualNumberEquiv_symm
 
+/- warning: quaternion.fst_im_k_dual_number_equiv_symm -> Quaternion.fst_imK_dualNumberEquiv_symm is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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_inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.fst.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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_inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.fst.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+Case conversion may be inaccurate. Consider using '#align quaternion.fst_im_k_dual_number_equiv_symm Quaternion.fst_imK_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem fst_imK_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imK.fst = d.fst.imK :=
   rfl
 #align quaternion.fst_im_k_dual_number_equiv_symm Quaternion.fst_imK_dualNumberEquiv_symm
 
+/- warning: quaternion.snd_re_dual_number_equiv_symm -> Quaternion.snd_re_dualNumberEquiv_symm is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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_inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.re.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.re.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+Case conversion may be inaccurate. Consider using '#align quaternion.snd_re_dual_number_equiv_symm Quaternion.snd_re_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_re_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).re.snd = d.snd.re :=
   rfl
 #align quaternion.snd_re_dual_number_equiv_symm Quaternion.snd_re_dualNumberEquiv_symm
 
+/- warning: quaternion.snd_im_i_dual_number_equiv_symm -> Quaternion.snd_imI_dualNumberEquiv_symm is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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_inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imI.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imI.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+Case conversion may be inaccurate. Consider using '#align quaternion.snd_im_i_dual_number_equiv_symm Quaternion.snd_imI_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_imI_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imI.snd = d.snd.imI :=
   rfl
 #align quaternion.snd_im_i_dual_number_equiv_symm Quaternion.snd_imI_dualNumberEquiv_symm
 
+/- warning: quaternion.snd_im_j_dual_number_equiv_symm -> Quaternion.snd_imJ_dualNumberEquiv_symm is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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_inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imJ.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imJ.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+Case conversion may be inaccurate. Consider using '#align quaternion.snd_im_j_dual_number_equiv_symm Quaternion.snd_imJ_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_imJ_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imJ.snd = d.snd.imJ :=
   rfl
 #align quaternion.snd_im_j_dual_number_equiv_symm Quaternion.snd_imJ_dualNumberEquiv_symm
 
+/- warning: quaternion.snd_im_k_dual_number_equiv_symm -> Quaternion.snd_imK_dualNumberEquiv_symm is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasNeg.{u1, u1} R R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (OfNat.mk.{u1} (DualNumber.{u1} R) 1 (One.one.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.hasOne.{u1, u1} R R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))))) (coeFn.{succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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(AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R 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_inst_1))))))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))))) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1)) (Quaternion.algebra.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.ring.{u1} R _inst_1))) (Quaternion.dualNumberEquiv._proof_4.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_5.{u1} R _inst_1) (Quaternion.dualNumberEquiv._proof_6.{u1} R _inst_1)) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Quaternion.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) d))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (d : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))), Eq.{succ u1} R (TrivSqZeroExt.snd.{u1, u1} R R (QuaternionAlgebra.imK.{u1} (DualNumber.{u1} R) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Neg.neg.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (OfNat.ofNat.{u1} (DualNumber.{u1} R) 1 (One.toOfNat1.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) 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(Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))))))) (Algebra.toModule.{u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R 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(CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Module.toDistribMulAction.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (AlgEquivClass.toAlgHomClass.{u1, u1, u1, u1} (AlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u1, u1, u1} R (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))))))))) (AlgEquiv.symm.{u1, u1, u1} R (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (DualNumber.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.one.{u1, u1} R R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (TrivSqZeroExt.neg.{u1, u1} R R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Quaternion.instRing.{u1} (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) (TrivSqZeroExt.semiring.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R (DualNumber.{u1} R) (TrivSqZeroExt.commRing.{u1, u1} R R _inst_1 (Ring.toAddCommGroup.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (TrivSqZeroExt.instAlgebraTrivSqZeroExtSemiringToSemiringTo_smulCommClassMulOppositeSemiringInstAlgebraMulOppositeSemiringIdOp_rightToSMulToZeroToAddMonoidToSMulZeroClassToZeroToCommMonoidWithZeroToSMulWithZeroToMonoidWithZeroToMulActionWithZeroToSMulToZeroLeftToMonoidToMulAction.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemigroup.isCentralScalar.{u1} R (NonUnitalCommRing.toCommSemigroup.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1))))) (TrivSqZeroExt.algebra'.{u1, u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (Semiring.toOppositeModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (SMulCommClass.opposite_mid.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R 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(Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.left.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))) (MonoidWithZero.toMulActionWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (IsScalarTower.right.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (IsScalarTower.opposite_mid.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toMul.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroOneClass.toMulZeroClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMulZeroOneClass.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)))))) (SMulZeroClass.toSMul.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (SMulWithZero.toSMulZeroClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (MulActionWithZero.toSMulWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))))) (Module.toMulActionWithZero.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Algebra.to_smulCommClass.{u1, u1} R (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.instRing.{u1} R _inst_1)) (Quaternion.instAlgebraQuaternionToOneToSemiringToCommSemiringToNegToRingToSemiringInstRing.{u1, u1} R R _inst_1 (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Quaternion.dualNumberEquiv.{u1} R _inst_1)) d))) (QuaternionAlgebra.imK.{u1} R (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Neg.neg.{u1} R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (TrivSqZeroExt.snd.{u1, u1} (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Quaternion.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_1))) d))
+Case conversion may be inaccurate. Consider using '#align quaternion.snd_im_k_dual_number_equiv_symm Quaternion.snd_imK_dualNumberEquiv_symmₓ'. -/
 @[simp]
 theorem snd_imK_dualNumberEquiv_symm (d : DualNumber (Quaternion R)) :
     (dualNumberEquiv.symm d).imK.snd = d.snd.imK :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -25,7 +25,7 @@ rigid motions in 3D space can be represented by dual quaternions of unit length.
 -/
 
 
-variable {R : Type _} [CommRing R]
+variable {R : Type*} [CommRing R]
 
 namespace Quaternion
 

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,15 +2,12 @@
 Copyright (c) 2023 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module algebra.dual_quaternion
-! leanprover-community/mathlib commit 536c256e5de12c1dc0352b6b60b44f3c6c5ef340
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.DualNumber
 import Mathlib.Algebra.Quaternion
 
+#align_import algebra.dual_quaternion from "leanprover-community/mathlib"@"536c256e5de12c1dc0352b6b60b44f3c6c5ef340"
+
 /-!
 # Dual quaternions